74.7.41 problem 41

Internal problem ID [16118]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 08:25:38 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 5.964 (sec). Leaf size: 105

dsolve([y(t)^4+(t^4-t*y(t)^3)*diff(y(t),t)=0,y(1) = 2],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\operatorname {RootOf}\left (6 i \pi \_Z431 +\operatorname {LambertW}\left (\_Z433 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z434 \right )}}{\left (-\frac {{\mathrm e}^{-3 \operatorname {RootOf}\left (6 i \pi \_Z431 +\operatorname {LambertW}\left (\_Z433 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z434 \right )}}{t^{3} \operatorname {LambertW}\left (\_Z433 , -\frac {{\mathrm e}^{-3 \operatorname {RootOf}\left (6 i \pi \_Z431 +\operatorname {LambertW}\left (\_Z433 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z434 \right )}}{t^{3}}\right )}\right )^{{1}/{3}}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{y[t]^4+(t^4-t*y[t]^3)*D[y[t],t]==0,{y[1]==2}},y[t],t,IncludeSingularSolutions -> True]
 

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